Effect of small roughness elements on thermal statistics of a turbulent boundary layer at moderate Reynolds number

A zero-pressure-gradient turbulent boundary layer flowing over a transitionally rough surface (24-grit sandpaper) with $k^{+}\approx 11$ and a momentum-thickness Reynolds number of approximately 2400 is studied using direct numerical simulation (DNS). Heat transfer between the isothermal rough surface and the turbulent flow with molecular Prandtl number $Pr=0.71$ is simulated. The dynamic multiscale approach developed by Araya et al. (J. Fluid Mech., vol. 670, 2011, pp. 581–605) is employed to prescribe realistic time-dependent thermal inflow boundary conditions. In general, the rough surface reduces mean and fluctuating temperature profiles with respect to the smooth surface flow when normalized by Wang & Castillo (J. Turbul., vol. 4, 2003, 006) inner/outer scaling. It is shown that the Reynolds analogy does not hold for $y^{+}